Unveiling the Complete Variant of Spherical Robots

Abstract

This study presents a systematic enumeration of spherical ($SO(3)$) type parallel robots' variants using an analytical velocity-level approach. These robots are known for their ability to perform arbitrary rotations around a fixed point, making them suitable for numerous applications. Despite their architectural diversity, existing research has predominantly approached them on a case-by-case basis. This approach hinders the exploration of all possible variants, thereby limiting the benefits derived from architectural diversity. By employing a generalized analytical approach through the reciprocal screw method, we systematically explore all the kinematic conditions for limbs yielding $SO(3)$ motion.Consequently, all 73 possible types of non-redundant limbs suitable for generating the target $SO(3)$ motion are identified. The approach involves performing an in-depth algebraic motion-constraint analysis and identifying common characteristics among different variants. This leads us to systematically explore all 73 symmetric and 5256 asymmetric variants, which in turn become a total of 5329, each potentially having different workspace capability, stiffness performance, and dynamics. Hence, having all these variants can facilitate the innovation of novel spherical robots and help us easily find the best and optimal ones for our specific applications.

Figures (1)

• Figure 1: Typical examples of spherical parallel robots obtained from Table \ref{['tab:limbs_spm']}: (a) 3-RSR with all joints' rotation centers meeting at the origin of the moving plate. (b) RCC with all joints' rotation centers meeting at the origin of the moving plate. (c) RRRRR with the last two joints intersecting at the center of the moving plate, while the first three joints intersect at a point other than the center of rotation. (d) 3-RRR intersecting at the center of the moving platform. (e) 3-RRS with all joints' rotation motions passing through the moving platform center. (f) The first three joints are parallel, while the last two joints meet at the center of the moving platform. (g) 3-RRS PM with joints meeting at a point different from the center of the moving platform. (h) 3-CRC with the first and last joints of all limbs meeting at the midpoint of the base plate. (i) 3-CRS with the axes of the first and third joints passing through the center of the base platform. (j) 3-UPC with U and C joints' axes passing through the origin of the base platform. (k) 3-CRU with the first and last joints' axes meeting at the center of the base platform.